基于蒙特卡罗方法的几何因子计算程序

应用蒙特卡罗方法求解几何因子,基于蒙特卡罗方法的几何因子计算程序使用C++语言编写,可用于任意位姿的各种尺寸的圆面探测器对圆面源几何因子的计算。该程序使用了方差减小技巧。通过与国际通用蒙特卡罗计算程序(MCNP5)的计算结果对比,该方法具有结果准确(误差较小)、计算速度快、使用方便等优点。最终使用该程序计算几何因子,与实验数据进行对比,成功验证了中子深度分布分析(NDP)能谱测量系统探测器位姿的准确性(误差5%以内),并对其移动位置进行修正,发现电机移动20mm大约会产生1mm的误差。     

CHMCK-一个复杂几何蒙特卡罗临界程序

为了用蒙特卡罗方法计算各种复杂几何核系统的有效增殖因子(K_eff),本工作给出了一种适于在复杂几何核系统内进行随机游动的方法,并用这一方法建立了相应的FORTRAN程序。     

混浊物质中光子传输的快速模拟与干涉特性分析

建立了混浊物质中低相干干涉系统的蒙特卡罗模型,结合相干面光强的高斯分布和低相干光源的相干条件,对干涉信号进行了数值分析.提出在蒙特卡罗计算的基线数据基础上快速模拟其他参数条件下干涉信号的方法.快速模拟结果与蒙特卡罗计算结果进行了比较,结果显示在满足前向散射条件下,两种方法所得模拟信号强度基本吻合.当各向异性因子g=0....     

MORSE-CG程序三维基准中子多孔隙度测井计算

用蒙特卡罗方法计算三维多孔隙度测井问题是一种比较有效的方法。本文给出增加了重新启动功能的MORSE-CG^[1]多功能蒙特卡罗程序计算孔隙度分别为1.0%和20.0%的基准中子测井问题的计算结果,以及其与MCNP和McDNL计算结果和计算时间的比较。比较显示三者在相同误差范围内的结果是一致的。     

蒙特卡罗粒子输运问题的全局降方差方法

精确获得中子通量的时间-空间-能量精细分布对于一类非定常粒子输运蒙特卡罗模拟至关重要.以零方差理论为基础,采取化整为零的策略,把蒙特卡罗方法与离散纵标方法相耦合,用近似重要函数指导蒙特卡罗模拟,给出一种实现蒙特卡罗全局降方差的计算方案.数值算例表明,该计算方案获得了全局降方差的效果.     

强流电子束自磁场对能量沉积的磁增强效应

一、引言 苏联的库尔恰托夫研究所最早报导了强流相对论电子束与等离子体相互作用过程中能量沉积的磁增强效应,该所于1976年发表了实验结果,增强因子是10;随后美国的Sandia实验室报导的磁增强因子是2—5;C.Peugnet和R.Bailly-Salins等人用强流电子束在薄金靶上做实验,获得了2—3倍的增强效应。他们的实验结果与理论计算结果是相符合的。本文主要是用蒙特卡罗方法对电子束在束自磁场的作用下的运动进行了模拟跟踪,计算了电子在薄铜靶中沉积能量的磁增强效应。     

蒙特卡罗与离散纵标耦合方法在压水堆堆腔漏束计算中的应用

为克服蒙特卡罗(MC)方法计算时间长和离散纵标(SN)方法复杂几何描述不精确的困难,采用SN-MC耦合计算流程,研究了基于蒙特卡罗方法和离散纵标方法的耦合方法。耦合方法的主要思想是根据离散纵标程序提供的中子角通量,利用接口程序计算出面源的分布概率,然后由修改后的源抽样子程序生成包括上下圆面源和圆柱面源的组合源,提供给蒙特卡罗程序进行计算分析。初步计算结果表明,该耦合方法是正确的,可用于压水堆堆腔漏束的计算分析。     

解深穿透问题的小区域蒙特卡罗方法

对于深穿透问题则一般蒙特卡罗方法存在一定的困难。本文提出了一个新的蒙特卡罗计算深穿透问题的小区域方法。在此基础上给出了两个小区域方法,即平几何小区域方法和球几何小区域方法,通过例子的实际计算表明,小区域方法是比较好的和可行的,克服了一般蒙特卡罗方法解深穿透问题的缺点。     

热辐射问题的迭代双向统计蒙特卡罗方法

为了进一步提高辐射传递因子的倒易性,本文提出了迭代双向统计蒙特卡罗方法。该方法将双向统计蒙特卡罗方法分解为归一化过程与双向统计过程,摆脱了传统迭代双向统计蒙特卡罗方法对等权抽样假设的依赖,进一步提高了辐射传递因子的倒易性。验证结果表明,迭代双向统计蒙特卡罗方法获得的辐射传递因子满足完整性,其倒易性误差的量级随双向统计迭代次数的增加而呈线性下降趋势。将该方法应用到含空腔结构的辐射/导热耦合边界平衡问题中,结果表明本文所建方法可以有效提高热辐射传输问题的求解精度,并且求解精度随着迭代次数的增加而提高。     

多物理耦合计算中动态输运问题高效蒙特卡罗模拟方法

多物理耦合计算在众多领域都有重要应用.如果其包含粒子输运过程,用蒙特卡罗方法模拟粒子输运常占据大部分的计算时间,因此多物理耦合计算中动态输运问题的高效蒙特卡罗模拟方法意义重大,其不可避免地依赖于大规模并行.基于动态输运问题的特点,本文提出了两种新方法:一是针对输运燃耗耦合计算的新型计数规约算法;二是动态输运计算样本数自适应算法.两种算法都能在保持计算结果基本不变的前提下使计算时间大幅减少,从而提高了效率.     

Quasiperiodic Heisenberg antiferromagnets in two dimensions

We describe some of the properties of 2d quantum quasiperiodic antiferromagnets as reported in studies that have been carried out in the last decade. Many results have been obtained for perfectly ordered as well as for disordered two dimensional bipartite quasiperiodic tilings. The theoretical methods used include spin wave theory, and renormalization group along with Quantum Monte Carlo simulations. These methods all show that the ground state of these unfrustrated antiferromagnets have Néel type order but with a highly complex spatial distribution of local staggered magnetization. The ground state properties, excitation energies and spatial dependence, structure factor, and local susceptibilities are presented and discussed. The effects of introducing geometrical disorder on the magnetic properties are discussed.     

Variational wave functions and their overlap with the ground state

An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The overlap is simply related to the area under the E(tau) curve, i.e., the energy as a function of imaginary time. This has important applications to, for example, quantum Monte Carlo simulations where the overlap becomes as a simple by-product of routine simulations. As a result, we find that the practical definition of a good variational wave function for quantum Monte Carlo simulations, i.e., fast convergence to the ground state, is equivalent to a good overlap with the actual ground state of the system.     

Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J1-J2 Heisenberg model

Restricted Boltzmann machine (RBM) has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system. On the other hand, as a shallow neural network, it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions. In order to find a way out of the dilemma, here, we propose to adopt the Green's function Monte Carlo (GFMC) method for which the RBM is used as a guiding wave function. To demonstrate the implementation and effectiveness of the proposal, we have applied the proposal to study the frustrated J₁-J₂ Heisenberg model on a square lattice, which is considered as a typical model with sign problem for quantum Monte Carlo simulations. The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results. This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.     

Validation of the Ability of Full Configuration Interaction Quantum Monte Carlo for Studying the 2D Hubbard Model

To validate the ability of full configuration interaction quantum Monte Carlo(FCIQMC) for studying the 2 D Hubbard model near half-filling regime, the ground state energies of a 4 x 4 square lattice system with various interaction strengths are calculated. It is found that the calculated results are in good agreement with those obtained by exact diagonalization(i.e., the exact values for a given basis set) when the population of psi particles(psips) is higher than the critical population required to correctly sample the ground state wave function. In addition, the variations of the average computational time per 20 Monte Carlo cycles with the coupling strength and the number of processors are also analyzed. The calculated results show that the computational efficiency of an FCIQMC calculation is mainly affected by the total population of psips and the communication between processors. These results can provide useful references for understanding the FCIQMC algorithm, studying the ground state properties of the 2 D Hubbard model for the larger system size by the FCIQMC method and using a computational budget as effectively as possible.     

Four-Parameter Scheme for Ground Level of Helium Atom

In this paper, the ground state wave function of four parameters is developed and the expression of the ground state level is derived for the helium atom when the radial Schrödinger equation of the helium atom is solved. The ground energy is respectively computed by the optimized algorithms of Matlab 7.0 and the Monte Carlo methods. Furthermore, the ground state wave function is obtained. Compared with the experiment value and the value with the variation calculus in reference, the results of this paper show that in the four-parameter scheme, not only the calculations become more simplified and precise, but also the radial wave function of the helium atom meets the space symmetry automatically in ground state.     

Ground-state properties of Fermi gases in the strongly interacting regime

The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.     

Charged-boson fluid at zero-temperature in the fractional dimensional space

In the fractional dimensional space, the ground state properties of the charged-boson fluid are studied in a theory which goes beyond the random phase approximation by including correlations through a static local-field-factor. The structure factor and static local field-factor are obtained in the self-consistent method. Qualitative agreement with the Monte Carlo results on static screening is achieved by imposing self-consistency on the compressibility of the fluid in addition to self-consistency on the structure factor. Using the structure factors obtained in these methods, several properties of the charged boson system such as the energy spectrum of elementary excitations, the pair-correlation function, the ground state energy, the pressure, the chemical potential and the compressibility are obtained in several dimensions including both integer and fractional values. Results obtained in the later method in two and three dimensional systems are close to the Monte Carlo and hypernetted-chain methods. The Wigner crystallisation in the lower dimensional system is found at higher density of bosons. However, it vanishes in any lower dimensional system whose dimension lies below 2.     

Accurate determination of tensor network state of quantum lattice models in two dimensions

We have proposed a novel numerical method to calculate accurately physical quantities of the ground state using the tensor network wave function in two dimensions. The tensor network wave function is determined by an iterative projection approach which uses the Trotter-Suzuki decomposition formula of quantum operators and the singular value decomposition of matrix. The norm of the wave function and the expectation value of a physical observable are evaluated by a coarse-grain tensor renormalization group approach. Our method allows a tensor network wave function with a high bond degree of freedom (such as D=8) to be handled accurately and efficiently in the thermodynamic limit. For the Heisenberg model on a honeycomb lattice, our results for the ground state energy and the staggered magnetization agree well with those obtained by the quantum Monte Carlo and other approaches.     

二维氢原子中的基态奇异特性数值精确对角化法

利用数值有限差分法处理二维氢原子的基态波函数时,计算结果发现其存在着数值奇异特性.本文通过构造一套具有正交完备性的离散贝塞尔基函数,并结合基于Lanczos技术的数值精确对角化方法研究二维氢原子中的基态波函数的数值奇异特性,得到的波函数数值解及其相应的本征能量均与解析结果相一致.这套新的完备的离散贝塞尔基函数,可以在研究一些波函数具有数值奇异特性的体系中发挥至关重要的作用.     

Recoil proton tagged knockout reaction for He

We report for the first time the discrimination of the core fragment knockout and valence nucleon knockout reaction mechanisms at medium energy range, by the use of the recoil proton tagging technique. Intense ⁸He beams at 82.3 MeV/u were supplied by the RIPS beam line at RIKEN, and impinged on both hydrogen and carbon targets. Recoil protons were detected in coincidence with the forward moving core fragments and neutrons. The core fragment knockout mechanism is identified through the polar angle correlation and checked by various kinematics relations. This mechanism may be used to extract the cluster structure information of unstable nuclei. On the other hand, with the selection of the tagged valence nucleon knockout mechanism, a narrower peak of ⁷He ground state is obtained. The extracted neutron spectroscopic factor Sn=0.512(18) is relatively smaller than the no-tagged one, and is in good agreement with the prediction of ab initio Green?s function Monte Carlo calculations.